| unifed.kappa {unifed} | R Documentation |
Cumulant generator of the unifed distribution
Description
Cumulant generator of the unifed distribution
Usage
unifed.kappa(theta)
unifed.kappa.prime(theta)
unifed.kappa.double.prime(theta)
unifed.kappa.prime.inverse(mu, ...)
unifed.kappa.prime.inverse.one(mu, tol = 1e-07, maxit = 1e+07)
Arguments
theta |
A numeric vector. |
mu |
A vector of numbers between 0 and 1 |
... |
Other parameters of |
tol |
Tolerance level. The algorithm stops if the proportional difference between the new and old value of an iteration is less or equal than this number. |
maxit |
Maximum number of iterations of the algorithm to look for convergence. |
Details
The cumulant generator of the unifed distribution is defined as
\kappa(\theta)=\left\{
\begin{array}{ll}
\log\left(\frac{e^\theta-1}{\theta}\right)& if \theta \neq
0\\
0 & \mbox{if }\theta=0
\end{array}
\right..
unifed.kappa.prime.inverse.one uses the
Newthon-Raphson method for finding the inverse of
unifed.kappa.prime for a single value.
Value
unifed.kappa returns a vector that contains the
cumulant generator of the unifed distribution applied to each
element of theta.
unifed.kappa.prime returns a vector that contains
the derivative of the cumulant generator of the unifed
distribution for each element of theta.
unifed.kappa.double.prime returns a vector that
contains the second derivative of the cumulant generator of the
unifed distribution for each element of theta.
unifed.kappa.prime.inverse returns a vector with
unifed.kappa.prime.inverse.one evaluated at every entry
of mu.
unifed.kappa.prime.inverse.one if the tolerance
level is reached within maxit iterations, the function
returns the value of the last iteration. Otherwise it returns
NA.
References
Quijano Xacur, O.A. The unifed distribution. J Stat Distrib App 6, 13 (2019). doi:10.1186/s40488-019-0102-6.
Jørgensen, Bent (1997). The Theory of Dispersion Models. Chapman & Hall, London.
Examples
unifed.kappa(1)
unifed.kappa(-5:5)
unifed.kappa.prime(4.5)
unifed.kappa.double.prime(0)
unifed.kappa.prime.inverse(0.5)
unifed.kappa.prime.inverse(c(0.1,0.7,0.9))